# GDDA: Semantic OOD Detection on Graphs under Covariate Shift via Score-Based Diffusion Models

arXiv: https://arxiv.org/abs/2410.17526 · HTML: https://mlsanity.com/paper/2410.17526/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 24 of its 31 references that are in the map.
- First posted on arXiv 23 Oct 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Open Domain Generalization with Domain-Augmented Meta-Learning](https://mlsanity.com/paper/2104.03620/) (2021)
- [Causal Attention for Interpretable and Generalizable Graph Classification](https://mlsanity.com/paper/2112.15089/) (2021)
- [Model-Based Domain Generalization](https://mlsanity.com/paper/2102.11436/) (2021)
- [Exploring Chemical Space with Score-based Out-of-distribution Generation](https://mlsanity.com/paper/2206.07632/) (2022)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [Energy-based Out-of-Distribution Detection for Graph Neural Networks](https://mlsanity.com/paper/2302.02914/) (2023)
- [Feed Two Birds with One Scone: Exploiting Wild Data for Both Out-of-Distribution Generalization and Detection](https://mlsanity.com/paper/2306.09158/) (2023)
- [GOOD-D: On Unsupervised Graph Out-Of-Distribution Detection](https://mlsanity.com/paper/2211.04208/) (2022)
- [Ensuring Fairness Beyond the Training Data](https://mlsanity.com/paper/2007.06029/) (2020)
- [Supervised Algorithmic Fairness in Distribution Shifts: A Survey](https://mlsanity.com/paper/2402.01327/) (2024)
- [Hierarchical Attentive Knowledge Graph Embedding for Personalized Recommendation](https://mlsanity.com/paper/1910.08288/) (2019)

## Built on by (most cited first, 5 of 5)

- [MADOD: Generalizing OOD Detection to Unseen Domains via G-Invariance Meta-Learning](https://mlsanity.com/paper/2411.02444/) (2024)
- [EigenScore: OOD Detection using Covariance in Diffusion Models](https://mlsanity.com/paper/2510.07206/) (2025)
- [Hypergraph-Based Dynamic Graph Node Classification](https://mlsanity.com/paper/2412.20321/) (2024)
- [Feature-Space Semantic Invariance: Enhanced OOD Detection for Open-Set Domain Generalization](https://mlsanity.com/paper/2411.07392/) (2024)
- [Out-of-Distribution Detection in Heterogeneous Graphs via Energy Propagation](https://mlsanity.com/paper/2505.03774/) (2025)

## Abstract (arXiv)

Out-of-distribution (OOD) detection poses a significant challenge for Graph Neural Networks (GNNs), particularly in open-world scenarios with varying distribution shifts. Most existing OOD detection methods on graphs primarily focus on identifying instances in test data domains caused by either semantic shifts (changes in data classes) or covariate shifts (changes in data features), while leaving the simultaneous occurrence of both distribution shifts under-explored. In this work, we address both types of shifts simultaneously and introduce a novel challenge for OOD detection on graphs: graph-level semantic OOD detection under covariate shift. In this scenario, variations between the training and test domains result from the concurrent presence of both covariate and semantic shifts, where only graphs associated with unknown classes are identified as OOD samples (OODs). To tackle this challenge, we propose a novel two-phase framework called Graph Disentangled Diffusion Augmentation (GDDA). The first phase focuses on disentangling graph representations into domain-invariant semantic factors and domain-specific style factors. In the second phase, we introduce a novel distribution-shift-controlled score-based generative diffusion model that generates latent factors outside the training semantic and style spaces. Additionally, auxiliary pseudo-in-distribution (InD) and pseudo-OOD graph representations are employed to enhance the effectiveness of the energy-based semantic OOD detector. Extensive empirical studies on three benchmark datasets demonstrate that our approach outperforms state-of-the-art baselines.